Research On Chattering-Free Terminal Sliding-Mode Control And Application In Induction Motor Speed Control

The control issue of uncertain systems has always been the focus of attention in the field of control,due to the matched and unmatched uncertainties in practical applications.Sliding-mode control?SMC?has been widely utilized in almost all theoretical and practical fields thanks to its robustness to matched uncertainties,however failed to deal with the unmatched uncertainties.Terminal Sliding-mode control exhibits various superior properties,such as finite-time convergence and smaller tracking errors compared to conventional SMC,while leads to singularity problem.Meanwhile,the unexpected chattering phenomenon is an inherent drawback of SMC which restricts its practical applications,hence the attenuation of chattering is an important issue.The control of induction motors?IMs?is a challenging issue owing to their nonlinearity and unmatched uncertainties.The IMs have been required by higher-performance industrial application,which makes control systems should achieve more satisfactory dynamic performance.So there is a strong need to improve the anti-disturbance,robustness and insensitivity of the IM control system and enhance the estimation performance of the rotor flux and speed.Therefore,there are profound theoretical significance and important practical values to further improve the terminal sliding mode control theory,solve the above control and observation problems,propose chattering-free SMC strategies with higher control performance and wider application range,and develop IMs drive systems with higher dynamic and static performance.To solve the singularity and chattering problems and deal with the unmatched uncertainties,this paper proposed a series of chattering–free full-order terminal SMC strategies.And based on the proposed control strategies,novel design methods of controllers and observers for speed control systems of IMs are proposed to improve their dynamic performance and robustness to load disturbances and parameter variations.The correctness and superiority of the proposed methods are verified by simulations and experiments.The specific contents are as follows.To overcome the problems of singularity and chattering in SMC,chattering–free full-order terminal SMC methods are proposed for a class of SISO and MIMO matched uncertain systems respectively.The singularity is solved by avoiding differentiating the exponential terms,and the chattering is attenuated by continuous control law based on full-order terminal sliding manifold.The innovation of the proposed method lies in that the value of proposed sliding manifold does not need to be measured or calculated owing to its known sign,which makes the structure simpler and easier to realize.The relative order of the ideal sliding mode is designed to be 0,which is different from the traditional form of greater than or equal to 1,so full-order dynamic characteristics of the control system are obtained rather than the traditional reduced-order ones.Consequently,smooth control signals are generated and the chattering induced by high-frequency switching control are attenuated.Compared with other SMC,the proposed method exhibited excellent performance of chattering-free,nonsingularity,fast convergence,high precision,strong robustness and easy implementation.Simulation experiments prove the advantages of the proposed methods.To compensate the unmatched uncertainties in MIMO systems,a backstepping based chattering-free full-order terminal sliding mode control strategy is proposed,which also serves as the theoretical basis for the SMC system of IMs.Conventional terminal SMC can only force the outputs of unmatched uncertain MIMO systems converge to the neighborhood near the equilibrium point in a finite time.In addition,most of the existing studies rely on strict conditions,such as the existence of right Moore–Penrose pseudo-inverse of gain matrix before the virtual control,and that the uncertainty must be H₂ norm-bounded or slow time-varying.In order to overcome these strict conditions and improve the control performance of terminal SMC,a virtual control law is firstly designed to compensate the unmatched uncertainties,and then the actual control signal is used to force the non-output system states to track the virtual control precisely,so that the outputs of the MIMO systems can converge to the equilibrium point rather than its neighborhood,and smooth virtual and actual control signals can be obtained thanks to the full-order sliding manifold and the chattering-free control law.Finally,simulation results validate the proposed methods.To improve the estimation accuracy and dynamic performance of observers for the rotor flux and speed of IMs,make them have the finite-time convergence and strong robustness to disturbance,and solve the problem of low SNR caused by chattering in conventional sliding-mode observer,this paper proposes rotor flux and speed observer design methods based on the proposed chattering–free full-order terminal sliding mode.Firstly,a novel design method of rotor flux observer is proposed for a speed-sensored FOC system,and then another observer design method for both the rotor flux and speed is proposed for a speed-sensorless FOC system.Finally,compared with other observers by simulation and experiments,the proposed observer design methods exhibit merits of rapid response,robustness to disturbance,nonsingularity,chattering free,continuous observation and high SNR,which can be directly applied into practical FOC systems of IMs without the filters.To develop high-performance speed control system of IMs,enhance its stability,tracking accuracy,dynamic performance and robustness to uncertainties,and eliminate the singularity and chattering in the conventional sliding mode controllers,this paper proposes a chattering–free full-order terminal SMC strategy for both the speed loop,flux loop and current loops of FOC systems.Firstly,the proposed control method for linear MIMO systems is extended to nonlinear MIMO system with unmatched uncertainties as the theoretical basis.In the design of outer-loop controllers,the reference currents are designed as virtual control signals to compensate the unmatched uncertainties such as load disturbance and parameter variations,and the tracking errors of speed and flux can converge to zero quickly in finite time.The chattering-free control law guarantees that the reference currents are smooth,which can be accurately tracked by the actual currents,so there is no chattering phenomenon.In the design of inner-loop controllers,the actual voltage control signal can force the steady-state errors of stator currents to converge to zero within finite time,and the tracking accuracy and dynamic performance are improved.Finally,combined with the proposed rotor flux/speed observers,the simulations and experiments prove that the proposed control system possess a higher-performance advantages.